Extended Cumulative Residual Entropy for Emergency Group Decision-Making Under Probabilistic Hesitant Fuzzy Environment

When an emergency occurs, there’s a massive challenge for experts to select the optimal emergency plan for disaster relief, because the decision-making process is full of uncertainty and fuzziness. This paper develops an emergency group decision-making method to help decision-makers choose the optimal emergency plan under probabilistic hesitant fuzzy environment. In the beginning, we offer a novel concept called probabilistic hesitant fuzzy cumulative residual entropy (PHFCRE) to measure the degree of uncertainty for probabilistic hesitant fuzzy elements (PHFEs). Then, incomplete probabilities for PHFEs are obtained by integrating the PHFCRE with the principle of maximum entropy. In addition, an enhanced weight determination method based on PHFCRE is proposed to obtain the attribute weights. Besides, to rank the alternatives, an enhanced satisfaction degree function based on PHFCRE is proposed. Finally, a real case concerning the snowstorm disaster is provided, and some comparison analyses are conducted to study the reasonability and practicality of the proposed method.